A projectile is fired horizontally from a 39 m cliff at 30m/s . Find the speed and velocity of the projectile when it strikes the ground.
Find vx
Find vy
Find v
To find the speed and velocity of the projectile when it strikes the ground, we can use the following equations:
1. Find the horizontal speed (vx):
Since the projectile is fired horizontally, there is no vertical acceleration acting on it. Hence, the horizontal component of velocity remains constant throughout the motion. Therefore, the horizontal speed (vx) is equal to the initial horizontal speed of the projectile, which is 30 m/s.
2. Find the vertical speed (vy):
To find the vertical speed (vy) when the projectile strikes the ground, we need to consider the height of the cliff and the time it takes for the projectile to fall.
Given:
Height of the cliff (h) = 39 m
We can use the equation for vertical displacement of an object in free-fall:
h = (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time.
Since the projectile was launched horizontally, the only time it takes to fall is the time it takes to reach the ground. We can find this time by using the following equation:
h = (1/2) * g * t^2
Rearranging the equation, we get:
t^2 = (2 * h) / g
Substituting the values, we have:
t^2 = (2 * 39) / 9.8
t^2 = 7.9591
t ≈ 2.82 s (taking the positive square root since time can't be negative)
Now, we can find the vertical speed (vy) when the projectile strikes the ground by multiplying the time by the acceleration due to gravity:
vy = g * t
vy = 9.8 * 2.82
vy ≈ 27.6 m/s (taking the positive value)
3. Find the absolute velocity (v):
Using the Pythagorean theorem, the square of the absolute velocity is the sum of the squares of the horizontal and vertical velocities:
v^2 = vx^2 + vy^2
Substituting the known values:
v^2 = 30^2 + 27.6^2
v^2 = 900 + 761.76
v^2 ≈ 1661.76
Taking the square root of both sides, we get:
v ≈ 40.77 m/s (rounded to two decimal places)
Therefore, the speed of the projectile when it strikes the ground is approximately 40.77 m/s. The horizontal velocity (vx) is 30 m/s, and the vertical velocity (vy) is approximately 27.6 m/s.